Floating offshore wind turbines (FOWTs) are generally located in the harsh deep-sea environment and are highly susceptible to extreme loads. In order to ensure the normal operation of FOWTs, this article takes the semi-submersible FOWT as an example, proposes a new double-rope mooring system, and studies the dynamic performance of the FOWT with the double-rope mooring system and its effectiveness in reducing the dynamic response of the wind turbine. At the same time, the tuned mass damper (TMD) is installed in the nacelle of the wind turbine, and the TMD parameters are optimized considering the space limitation of the nacelle by limiting the TMD’s stroke, which further reduces the dynamic response of the FOWT and improves its stability. Numerical simulation and analytical studies show that the new double-rope mooring system can reduce the dynamic response of the wind turbine to a greater extent than the traditional single-rope mooring system. Considering the stroke restriction, the control performance of TMD will be slightly weakened, but it is more in line with the actual engineering requirements. Compared with the original FOWT, the proposed new type of FOWT has better dynamic stability and has the prospect of extending to real engineering applications.